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Polynomial constraint-solving plays a prominent role in several areas of engineering and software verification. In particular, polynomial constraint solving has a long and successful history in the development of tools for proving termination of programs. Well-known and very efficient techniques, like SAT algorithms and tools, have been recently proposed… (More)

Although theoretically it is very powerful, the semantic path ordering (SPO) is not so useful in practice, since its monotonicity has to be proved by hand for each concrete term rewrite system (TRS). In this paper we present a monotonic variation of SPO, called MSPO. It characterizes termination, i.e., a TRS is terminating if and only if its rules are… (More)

Context-sensitive rewriting (CSR) is a simple restriction of rewriting which can be used e.g. for modelling non-eager evaluation in programming languages. Many times termination is a crucial property for program veriication. Hence, developing tools for automatically proving termination of CSR is necessary. All known methods for proving termination of (CSR)… (More)

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering… (More)

There is an increasing use of ((rst-and higher-order) rewrite rules in many programming languages and logical systems. The recursive path ordering (RPO) is a well-known tool for proving termination of such rewrite rules in the rst-order case Der82]. However, RPO has some weaknesses. For instance, since it is a simpliication ordering, it can only handle… (More)

In contrast to the current general way of developing tools for proving termination automatically, this paper intends to show an alternative program based on using on the one hand the theory of term orderings to develop powerful and widely applicable methods and on the other hand constraint based techniques to put them in practice. In order to show that this… (More)

In most termination tools two ingredients, namely recursive path orderings (RPO) and polynomial interpretation orderings (POLO), are used in a consecutive disjoint way to solve the final constraints generated from the termination problem. In this paper we present a simple ordering that combines both RPO and POLO and defines a family of orderings that… (More)

We will show how to translate the termination proof of a term rewrite system (TRS) using the Monotonic Semantic Path Ordering (MSPO) [BFR00] into a constraint solving problem. By using the definition of MSPO a disjunction of constraints is obtained, such that, if any of these constraints can be solved, then the TRS is proved to be terminating. Our… (More)

TERMPTATION (TERMination Proof Techniques automATION) is a fully automated system for proving termination of term rewrite systems (TRS) which is based on the monotonic semantic path ordering method (MSPO) [BFR00] and its translation to an ordering constraint solving problem [BR03], called the MSPO-constraint method (see [Bor03] for a detailed description).… (More)